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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On some rings whose modules have maximal submodules


Author: V. P. Camillo
Journal: Proc. Amer. Math. Soc. 50 (1975), 97-100
MSC: Primary 16A48
MathSciNet review: 0382343
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Abstract: It is shown that a principal right ideal domain, having the property that every right $ R$ module has a maximal submodule must be simple. Strong conditions satisfied by these rings are deduced giving evidence for the conjecture that they must be $ V$-rings. We also generalize an example of Faith by showing that a subring of an infinite dimensional full linear ring, which contains the socle of that ring is never a left $ V$-ring.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0382343-9
PII: S 0002-9939(1975)0382343-9
Keywords: Maximal submodule, principal ideal ring, simple ring, $ V$-ring
Article copyright: © Copyright 1975 American Mathematical Society